FINANC 3000 1st Edition Lecture 3 Outline of Last Lecture I. Balance SheetII. Income StatementIII. Statement of Cash FlowsIV. Statement of Retained EarningsOutline of Current Lecture I. Organizing Cash FlowsII. Different types of InterestIII. Future ValueIV. The Power of CompoundingV. Present ValueCurrent LectureIntroduction- Time Value of Money basic concept:o $1 today is worth more than $1 next year- Inflation reducing the value- How much more is a dollar today than a dollar tomorrowOrganizing Cash Flows- Cash flow timing key to successful business operations- Cash flow analysiso Inflow = cash received (positive number)o Outflow = cash going out (negative number)Simple Interest- If you invest $100 at 5% for a year, how much will you have after 1 year?o $105 = $100 principal + $5 interest $105 = $100 + $100 x .05- $105 = $100 x (1 + .05)o $105 = $100 x (1.05)o Value in 1 year = today’s value x (1 +interest rate)These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute. FV = PV x (1+i)Compound Interest- The interest on both the principal and its unpaid interest added to it at stated intervals- Suppose you leave $100 for two years at 5 percent interest compounded annuallyo After two years you would have: $110.25 = [$100 x (1.05)] x (1.05)- $110.25 = $100 x (1.05) ^2o Value in Year 2 = Today’s Value x Interest in Year 1 x Interest in Year 2Compounding and Future Value- Concept: Compoundingo Interest is earned on both principal and interesto Today’s cash flow + interest on principal and interest on interest = value in 2 years FV = PV x (1 + i) ^NThe Power of Compounding- Compound interest is a powerful wealth-building tool -> exponential growth- What would be the value of $100 in 15 years with 5% interest?o $100 x (1.05) ^ 15 = 207.89o Total interest in 15 years $207.89 - $100= $107.89o Simple interest 15 x $5 = $75o Compound interest $107.89 - $75 = $32.89Compounding at Different Rates- EX: The bank will pay 5% in Year 1 and 4% in Year 2- $100 x 1.05 x 1.04 = $109.20- FV = PV x (1+i-period 1)x(1+i-period 2)x(1+i-period N)Compounding Interest: Compounding Periods- In finance we use compound interest- There are alternatives to annual compoundingo Many corporate and government bonds pay interest twice a year and have semiannual compoundingo Most mortgage loans and auto loans have monthly payments and thus monthly compoundingo The limiting case is continuous compounding- The formula for finding the future value of an amount of money (PV) invested at i percent compounded m times per year for n years is:o FV = PV [1 + (i/m)] ^ (nxm)Present Value- Opposite of Future Valueo Future value = compoundingo Present value = discounting- Value today of sum expected to be received in the future- Present value of next period’s cash flow = next period’s value/ one period discountingo PV = [FV/(1+i)]- EXo Bank pays $105 in year at 5% interest. How much did you deposit? $105 = (1.05) = $100Present value with Multiple Periods- Concept: Discounting- Reverse of compounding over multiple periodso PV = FV x [1/(1+i)^N = FV / (1+i)^N- Let’s assume you will receive $100 in 5 years and current market rates are 5%. How much should you pay for that opportunity?o PV = $100/ (1.05)^5 = $100/1.2763 = $78.35Present Value with Multiple Rates- Concept: Discounting- Value today of sum expected to be received in future – variable rates of interest over timeo PV = [FV/(1+i-period one)x(1+i-period 2)x(1+i-period 3)x(1+i-period N)- How much would you pay to receive $100 in 3 years if Year 1 interest is 5%, year 2 interest is 6%, and year 3 interest is 7%?o PV = $100/ (1.05 x 1.06 x 1.07) =